Preparation
Show code
library(tidyverse)
library(ggtext)
library(spatstat.core)
library(patchwork)
theme_set(theme_light(base_size = 10, base_family = "Open Sans"))
theme_update(
panel.grid.major = element_line(size = .3),
panel.grid.minor = element_blank(),
plot.title = element_markdown(size = 18),
plot.title.position = "plot",
plot.margin = margin(rep(25, 4))
)
Research Question
- Predictive power of the acoustic monitoring
Is the predictive power of the current acoustic monitoring sufficient enough to estimate the true number of killed bats?
Predictions
The predictive power of the acoustic monitoring for the extrapolation of the expected number of stroke victims is decreasing
in case the crossing bats are not distributed uniformly or randomly.
with increasing length of the rotor blades.
for species with high-frequency echo calls.
Open Questions
- wie die Dichte skalieren zwischen großen und kleinen Windrädern?
- z.B. von innen nach außen abhängig von relativer oder absoluter Distanz zum Mittelpunkt?
- globale oder lokale Anzahl an Fledermäusen konstant halten?
Inputs
We have the following parameters we can vary:
- length of rotor blades (
radius_rotor) - 60 m versus 33 m- determines area of wind turbine (
area_rotoraspi * radius_rotor^2)
- determines area of wind turbine (
- proportion of area covered by acoustic monitoring (
proportion_covered)- determines area of acoustic monitoring (
area_monitoredasarea_rotor * proportion_covered) - determines radius to detect bars (
radius_monitoredassqrt(area_monitored / pi))
- determines area of acoustic monitoring (
- number of bats simulated (
n)- could be either total (for now) or number monitored (maybe later)
Show code
## radius circle (~ length rotor blades)
radius_rotor <- 1
## % area covered by acoustic monitoring
proportion_covered <- .05
## radius acoustic monitoring via % area covered + length rotor blades
area_rotor <- pi * radius_rotor^2
area_monitored <- area_rotor * proportion_covered
radius_monitored <- sqrt(area_monitored / pi)
## mask for window
circle <- disc(
radius = radius_rotor,
centre = c(0, 0),
mask = FALSE,
npoly = 5000
)
## number of points (~ bats)
n <- 500
Circular Distributions
Uniform Sunflower Function
from StackOverflow
Show code
sunflower <- function(n, alpha = 2, geometry = c('planar','geodesic')) {
b <- round(alpha*sqrt(n)) # number of boundary points
phi <- (sqrt(5)+1)/2 # golden ratio
r <- radius(1:n,n,b)
theta <- 1:n * ifelse(geometry[1] == 'geodesic', 360*phi, 2*pi/phi^2)
tibble(
x = r*cos(theta),
y = r*sin(theta)
)
}
radius <- function(k,n,b) {
ifelse(
k > n-b,
1,
sqrt(k-1/2) / sqrt(n-(b+1)/2)
)
}
# example:
sunflower(500, 2, 'planar')
# A tibble: 500 x 2
x y
<dbl> <dbl>
1 -0.0239 0.0219
2 0.00490 -0.0559
3 0.0440 0.0575
4 -0.0843 -0.0149
5 0.0820 -0.0521
6 -0.0279 0.104
7 -0.0538 -0.104
8 0.118 0.0430
9 -0.123 0.0509
10 0.0598 -0.128
# ... with 490 more rowsGenerate Point Patterns
Show code
## fix random number genreration to ensure reproducibility
set.seed(12345)
## random
pp_rand <- spatstat.core::rpoint(n, win = circle)
df_rand <- as.data.frame(pp_rand) %>% mutate(dist = x^2 + y^2)
## uniform
pp_unif <- spatstat.core::runifpoint(n, win = circle)
df_unif <- as.data.frame(pp_unif) %>% mutate(dist = x^2 + y^2)
df_sunf <- sunflower(n, 1, 'planar') %>% mutate(dist = x^2 + y^2)
## directional: inner > outer
pp_inn <- rpoint(n, function(x,y) {1 - (abs(-x^2 - y^2)) + .01}, win = circle)
df_inn <- as.data.frame(pp_inn) %>% mutate(dist = x^2 + y^2)
## directional: outer > inner
pp_out <- rpoint(n, function(x,y) {(abs(x^2 + y^2)) + .01}, win = circle)
df_out <- as.data.frame(pp_out) %>% mutate(dist = x^2 + y^2)
## directional: bottom > top
pp_btm1 <- rpoint(n, function(x,y) {100 * exp(-1*y)}, win = circle)
df_btm1 <- as.data.frame(pp_btm1) %>% mutate(dist = x^2 + y^2)
pp_btm2 <- rpoint(n, function(x,y) {100 * exp(-2*y)}, win = circle)
df_btm2 <- as.data.frame(pp_btm2) %>% mutate(dist = x^2 + y^2)
pp_btm3 <- rpoint(n, function(x,y) {100 * exp(-3*y)}, win = circle)
df_btm3 <- as.data.frame(pp_btm3) %>% mutate(dist = x^2 + y^2)
pp_btm4 <- rpoint(n, function(x,y) {100 * exp(-4*y)}, win = circle)
df_btm4 <- as.data.frame(pp_btm4) %>% mutate(dist = x^2 + y^2)
pp_btm5 <- rpoint(n, function(x,y) {100 * exp(-5*y)}, win = circle)
df_btm5 <- as.data.frame(pp_btm5) %>% mutate(dist = x^2 + y^2)
pp_btm6 <- rpoint(n, function(x,y) {100 * exp(-6*y)}, win = circle)
df_btm6 <- as.data.frame(pp_btm6) %>% mutate(dist = x^2 + y^2)
pp_btm7 <- rpoint(n, function(x,y) {100 * exp(-7*y)}, win = circle)
df_btm7 <- as.data.frame(pp_btm7) %>% mutate(dist = x^2 + y^2)
pp_btm8 <- rpoint(n, function(x,y) {100 * exp(-8*y)}, win = circle)
df_btm8 <- as.data.frame(pp_btm8) %>% mutate(dist = x^2 + y^2)
pp_btm9 <- rpoint(n, function(x,y) {100 * exp(-9*y)}, win = circle)
df_btm9 <- as.data.frame(pp_btm9) %>% mutate(dist = x^2 + y^2)
pp_btm10 <- rpoint(n, function(x,y) {100 * exp(-10*y)}, win = circle)
df_btm10 <- as.data.frame(pp_btm10) %>% mutate(dist = x^2 + y^2)
Plots Point Patterns
Show code
plot_dist <- function(data, title, color = TRUE) {
base <-
ggplot(as.data.frame(circle), aes(x, y)) +
geom_path(color = "black", alpha = .33, size = 2) +
coord_fixed() +
scale_x_continuous(limits = c(-1, 1)) +
scale_y_continuous(limits = c(-1, 1))
if (isTRUE(color)) {
base +
geom_point(data = data, aes(color = dist), alpha = .7) +
scale_color_gradient(low = "#003F4C", high = "#B200B2", guide = "none") +
ggtitle(title)
} else {
base +
geom_point(data = data, alpha = .7) +
ggtitle(title)
}
}
Distribution Scenarios
Show code
## no color versions ###########################################################
## random
gg_rand_nc <- plot_dist(df_rand, "**Random**", color = FALSE)
## uniform
#gg_unif_nc <- plot_dist(df_unif, "**Uniform** (?)", color = FALSE)
gg_sunf_nc <- plot_dist(df_sunf, "**Uniform** (sunflower)", color = FALSE)
## directional: inner > outer
gg_inn_nc <- plot_dist(df_inn, "**Inner to Outer**", color = FALSE)
## directional: outer > inner
gg_out_nc <- plot_dist(df_out, "**Outer to Inner**", color = FALSE)
## directional: bottom > top
gg_btm1_nc <- plot_dist(df_btm1, "**Bottom to Top** (exp(-y))", color = FALSE)
gg_btm2_nc <- plot_dist(df_btm2, "**Bottom to Top** (exp(-2*y))", color = FALSE)
gg_btm3_nc <- plot_dist(df_btm3, "**Bottom to Top** (exp(-3*y))", color = FALSE)
gg_btm4_nc <- plot_dist(df_btm4, "**Bottom to Top** (exp(-4*y))", color = FALSE)
gg_btm5_nc <- plot_dist(df_btm5, "**Bottom to Top** (exp(-5*y))", color = FALSE)
gg_btm6_nc <- plot_dist(df_btm6, "**Bottom to Top** (exp(-6*y))", color = FALSE)
gg_btm7_nc <- plot_dist(df_btm7, "**Bottom to Top** (exp(-7*y))", color = FALSE)
gg_btm8_nc <- plot_dist(df_btm8, "**Bottom to Top** (exp(-8*y))", color = FALSE)
gg_btm9_nc <- plot_dist(df_btm9, "**Bottom to Top** (exp(-9*y))", color = FALSE)
gg_btm10_nc <- plot_dist(df_btm10, "**Bottom to Top** (exp(-10*y))", color = FALSE)
## panel
(gg_sunf_nc | gg_btm2_nc | gg_inn_nc) / (gg_rand_nc | gg_btm5_nc | gg_out_nc)
Show code
ggsave("plots/circular_distributions_nc.png", width = 15, height = 10, dpi = 700)
Distribution Scenarios Colored by Distance
Show code
## colored versions ############################################################
## random
gg_rand <- plot_dist(df_rand, "**Random**")
## uniform
#gg_unif <- plot_dist(df_unif, "**Uniform** (?)")
gg_sunf <- plot_dist(df_sunf, "**Uniform** (sunflower)")
## directional: inner > outer
gg_inn <- plot_dist(df_inn, "**Inner to Outer**")
## directional: outer > inner
gg_out <- plot_dist(df_out, "**Outer to Inner**")
## directional: bottom > top
gg_btm1 <- plot_dist(df_btm1, "**Bottom to Top** (exp(-y))")
gg_btm2 <- plot_dist(df_btm2, "**Bottom to Top** (exp(-2*y))")
gg_btm3 <- plot_dist(df_btm3, "**Bottom to Top** (exp(-3*y))")
gg_btm4 <- plot_dist(df_btm4, "**Bottom to Top** (exp(-4*y))")
gg_btm5 <- plot_dist(df_btm5, "**Bottom to Top** (exp(-5*y))")
gg_btm6 <- plot_dist(df_btm6, "**Bottom to Top** (exp(-6*y))")
gg_btm7 <- plot_dist(df_btm7, "**Bottom to Top** (exp(-7*y))")
gg_btm8 <- plot_dist(df_btm8, "**Bottom to Top** (exp(-8*y))")
gg_btm9 <- plot_dist(df_btm9, "**Bottom to Top** (exp(-9*y))")
gg_btm10 <- plot_dist(df_btm10, "**Bottom to Top** (exp(-10*y))")
## panel
(gg_sunf | gg_btm2 | gg_inn) / (gg_rand | gg_btm5 | gg_out)
Show code
ggsave("plots/circular_distributions.png", width = 15, height = 10, dpi = 700)
Variations of Bottom to Top Distributions
Show code
## panel bottom > top
(gg_btm1_nc | gg_btm2_nc | gg_btm3_nc | gg_btm4_nc | gg_btm5_nc) / (gg_btm6_nc | gg_btm7_nc | gg_btm8_nc | gg_btm9_nc | gg_btm10_nc)
Show code
ggsave("plots/circular_distributions_btms_nc.png", width = 24, height = 10, dpi = 700)
Distribution Scenarios Colored by Distance
Show code
## panel bottom > top
(gg_btm1 | gg_btm2 | gg_btm3 | gg_btm4 | gg_btm5) / (gg_btm6 | gg_btm7 | gg_btm8 | gg_btm9 | gg_btm10)
Show code
ggsave("plots/circular_distributions_btms.png", width = 24, height = 10, dpi = 700)
Plots Proportion Monitored
Show code
plot_monitoring <- function(gg, data, circle_monitored) {
gg +
geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(data, dist < radius_monitored^2), color = "orange2")
}
Show code
plot_monitoring_all <- function(proportion_covered, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5) {
## radius acoustic monitoring via % area covered + length rotor blades
area_rotor <- pi * radius_rotor^2
area_monitored <- area_rotor * proportion_covered * 2
## times 2 because we only use the lower half of the circle = half of the area later
radius_monitored <- sqrt(area_monitored / pi)
circle_monitored <- disc(
radius = radius_monitored,
centre = c(0,0),
mask = FALSE,
npoly = 5000
)
circle_half_monited <-
as.data.frame(circle_monitored) %>%
filter(y <= 0)
## random
gg_rand_r <- gg_rand_nc +
geom_path(data = circle_half_monited, color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(df_rand, dist < radius_monitored^2 & y <= 0), color = "orange2")
## uniform
# gg_unif_r <- gg_unif_nc +
# geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
# geom_point(data = filter(df_unif, dist < radius_monitored^2), color = "orange2")
gg_sunf_r <- gg_sunf_nc +
geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(df_sunf, dist < radius_monitored^2), color = "orange2")
## directional: inner > outer
gg_inn_r <- gg_inn_nc +
geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(df_inn, dist < radius_monitored^2), color = "orange2")
## directional: outer > inner
gg_out_r <- gg_out_nc +
geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(df_out, dist < radius_monitored^2), color = "orange2")
## bottom > top
gg_btm2_r <- gg_btm2_nc +
geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(df_btm2, dist < radius_monitored^2), color = "orange2")
gg_btm5_r <- gg_btm5_nc +
geom_path(data = as.data.frame(circle_monitored), color = "orange2", alpha = .2, size = 1.5) +
geom_point(data = filter(df_btm5, dist < radius_monitored^2), color = "orange2")
## panel
p <- (gg_sunf_r | gg_btm2_r | gg_inn_r) / (gg_rand_r | gg_btm5_r | gg_out_r)
}
Monitoring Covers 50%
Show code
(panel_monitored <- plot_monitoring_all(
proportion_covered = .5, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5
))
Show code
ggsave("plots/circular_distributions_area_monitored_50.png", width = 15, height = 10, dpi = 700)
Monitoring Covers 40%
Show code
(panel_monitored <- plot_monitoring_all(
proportion_covered = .4, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5
))
Show code
ggsave("plots/circular_distributions_area_monitored_40.png", width = 15, height = 10, dpi = 700)
Monitoring Covers 30%
Show code
(panel_monitored <- plot_monitoring_all(
proportion_covered = .3, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5
))
Show code
ggsave("plots/circular_distributions_area_monitored_30.png", width = 15, height = 10, dpi = 700)
Monitoring Covers 20%
Show code
(panel_monitored <- plot_monitoring_all(
proportion_covered = .2, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5
))
Show code
ggsave("plots/circular_distributions_area_monitored_20.png", width = 15, height = 10, dpi = 700)
Monitoring Covers 10%
Show code
(panel_monitored <- plot_monitoring_all(
proportion_covered = .1, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5
))
Show code
ggsave("plots/circular_distributions_area_monitored_10.png", width = 15, height = 10, dpi = 700)
Monitoring Covers 5%
Show code
(panel_monitored <- plot_monitoring_all(
proportion_covered = .05, df_rand, df_sunf, df_inn, df_out, df_btm_2, df_btm_5
))
Show code
ggsave("plots/circular_distributions_area_monitored_05.png", width = 15, height = 10, dpi = 700)
Session Info
Show code
Sys.time()
[1] "2021-11-22 14:31:49 CET"Show code
R version 4.1.0 (2021-05-18)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19043)
Matrix products: default
locale:
[1] LC_COLLATE=German_Germany.1252 LC_CTYPE=German_Germany.1252
[3] LC_MONETARY=German_Germany.1252 LC_NUMERIC=C
[5] LC_TIME=German_Germany.1252
system code page: 65001
attached base packages:
[1] stats graphics grDevices utils datasets methods
[7] base
other attached packages:
[1] patchwork_1.1.1 spatstat.core_2.3-0 rpart_4.1-15
[4] nlme_3.1-152 spatstat.geom_2.3-0 spatstat.data_2.1-0
[7] ggtext_0.1.1 forcats_0.5.1 stringr_1.4.0
[10] dplyr_1.0.7 purrr_0.3.4 readr_2.0.2
[13] tidyr_1.1.4 tibble_3.1.5 ggplot2_3.3.5
[16] tidyverse_1.3.1
loaded via a namespace (and not attached):
[1] fs_1.5.0 spatstat.sparse_2.0-0 lubridate_1.8.0
[4] httr_1.4.2 tools_4.1.0 backports_1.2.1
[7] bslib_0.3.1 utf8_1.2.2 R6_2.5.1
[10] DBI_1.1.1 mgcv_1.8-35 colorspace_2.0-2
[13] withr_2.4.2 tidyselect_1.1.1 downlit_0.2.1
[16] compiler_4.1.0 textshaping_0.3.6 cli_3.0.0
[19] rvest_1.0.2 xml2_1.3.2 labeling_0.4.2
[22] sass_0.4.0 scales_1.1.1 goftest_1.2-3
[25] systemfonts_1.0.3 digest_0.6.28 spatstat.utils_2.2-0
[28] rmarkdown_2.11 pkgconfig_2.0.3 htmltools_0.5.2
[31] highr_0.9 dbplyr_2.1.1 fastmap_1.1.0
[34] rlang_0.4.12 readxl_1.3.1 rstudioapi_0.13
[37] farver_2.1.0 jquerylib_0.1.4 generics_0.1.0
[40] jsonlite_1.7.2 distill_1.3 magrittr_2.0.1
[43] Matrix_1.3-3 Rcpp_1.0.7 munsell_0.5.0
[46] fansi_0.5.0 abind_1.4-5 lifecycle_1.0.1
[49] stringi_1.7.5 yaml_2.2.1 grid_4.1.0
[52] crayon_1.4.1 deldir_1.0-5 lattice_0.20-44
[55] haven_2.4.3 splines_4.1.0 tensor_1.5
[58] gridtext_0.1.4 hms_1.1.1 knitr_1.36
[61] pillar_1.6.4 markdown_1.1 reprex_2.0.1
[64] glue_1.4.2 evaluate_0.14 modelr_0.1.8
[67] vctrs_0.3.8 tzdb_0.1.2 cellranger_1.1.0
[70] gtable_0.3.0 polyclip_1.10-0 assertthat_0.2.1
[73] xfun_0.27 broom_0.7.9 ragg_1.1.3
[76] ellipsis_0.3.2